Quantization Based Hash Mapping Embedding

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Quantization Based Hash Mapping Embedding

• Presented by Ning Liu

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General Data Hiding Scheme
U
Y
X
Attack (N)
Recovered Data (W)
Embedded Data (W)
Tradeoff in 3 aspects

• minimizing the distortion in the host image due
  to embedding,
• maximizing the robustness of information hiding,
• maximizing the capacity of the scheme

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Costas Idea
P the transmitter power constraint, Z the
channel noise
W the hiding-data
S side information (host image)
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Costas Scheme
The channel is AWGN and the signal (side
information, S) is i.i.d. Gaussian distributed.
The capacity is given as
where P and N represent the transmitter power
constraint and the variance of the channel noise
respectively . The space of codewords must be of
the form
The ideal Costa scheme (ICS) is not practical
due to the large size of the random codebook
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Secure Quantization based Data-Embedding

• We study the combined security, robustness and
  host distortion enhancement of quantization index
  modulation (QIM) based data hiding for multimedia
  security.
• We compare our algorithm with the one proposed by
  Wu 1, who shows that through a lookup table
  (LUT) of nontrivial run that maps quantized
  multimedia features randomly to binary data, the
  probability of detection error can be
  considerably smaller than the traditional
  quantization embedding.
• We note that in her algorithm we would have to
  overlook the distortion constraint to achieve
  robustness.
• On the contrary, in the proposed algorithm, we
  propose to elegantly trade off security,
  robustness, without increasing distortion to the
  host.
• we show that the proposed hash mapping embedding
  provides joint enhancement of security and
  robustness over the LUT embedding while
  maintaining the distortion constraint.

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LUT Embedding-1

• The encoder generates a LUT before hand, denoted
  by T(.).
• In a random manner, the LUT maps every quantizer
  representation value to a binary 0 or a binary
  1, while setting the probability of either
  mapping at 0.5.
• To embed a 0 (or a 1), the feature is
  quantized to the closest representation value
  that is mapped to a 0 (or a 1) as seen in
  equation below.
• Here, d min dQuant(x)-X0 s.t.
  T(Quant(x)/q)b
• Conversely, the extraction is done by looking up
  the LUT as seen in equation below.
• The number of 1 and 0 mappings have to be
  constrained in the LUT to avoid excessive
  modification to the host.

q
d
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Security Strength of LUT Scheme

• The security strength of LUT depends on the
  maximum run, r.
• a) A Markov chain model for LUT table generation,
  where the transition probability is ½ for solid
  arrow lines and 1 for dash arrow lines.
• b) The entropy rate of LUT table as a function of
  the maximum allowable run r.

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Distortion Analysis of LUT Scheme
..
X
X
X
O
X
X
O
X
O
O

• If the maximum allowable run of 1 and 0 is
  denoted by r, and if it is set to 1, we note that
  this leads to a maximum of two possible tables as
  seen below.
• It is noted that the MSE distortion for odd-even
  quantization based scheme is q2/3 as compared to
  the MSEA distortion by Wus algorithm (maximum
  allowable run r2) is q2/2. For larger r, MSEA
  will be even larger than q2/2
• We note that the security enhancement of LUT
  embedding is at the cost of distortion caused by
  embedding

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Proposed scheme

• Wu in 1, states that the security strength is
  achieved by LUT embedding at the cost of the
  robustness in terms of probability of detection
  error, especially in a high WNR range. In this
  paper, we propose a new scheme, which can achieve
  security strength without sacrificing the
  robustness, while maintaining the distortion
  constraint.